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1. Transformation matrix - Wikipedia
Link: https://en.wikipedia.org/wiki/Transformation_matrix
Description: If one has a linear transformation in functional form, it is easy to determine the transformation matrix A by transforming each of the vectors of the standard basis by T, then inserting the result into the columns of a matrix. In other words, For example, the function is a linear transformation.
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2. Translation (geometry) - Wikipedia
Link: https://en.wikipedia.org/wiki/Translation_(geometry)
Description: To translate an object by a vector, each homogeneous vector (written in homogeneous coordinates) can be multiplied by this translation matrix: T v = [ 1 0 0 v x 0 1 0 v y 0 0 1 v z 0 0 0 1 ] {\displaystyle T_{\mathbf {v} }={\begin{bmatrix}1&0&0&v_{x}\\0&1&0&v_{y}\\0&0&1&v_{z}\\0&0&0&1\end{bmatrix}}}
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3. 3.1: Matrix Transformations - Mathematics LibreTexts
Link: https://math.libretexts.org/Bookshelves/Linear_Algebra/Interactive_Linear_Algebra_(Margalit_and_Rabinoff)/03%3A_Linear_Transformations_and_Matrix_Algebra/3.01%3A_Matrix_Transformations
Description: Sep 17, 2022 · Learn examples of matrix transformations: reflection, dilation, rotation, shear, projection. Understand the vocabulary surrounding transformations: domain, codomain, range. Understand the domain, codomain, and range of a matrix transformation. Pictures: common matrix transformations.
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4. Geometric Transformations - Michigan Technological University
Link: https://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/geometry/geo-tran.html
Description: A rotation matrix and a translation matrix can be combined into a single matrix as follows, where the r's in the upper-left 3-by-3 matrix form a rotation and p, q and r form a translation vector. This matrix represents rotations followed by a translation. You can apply this transformation to a plane and a quadric surface just as what we did for ...
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5. Transformation Matrix: Explanation, Types, Properties with …
Link: https://testbook.com/maths/transformation-matrix
Description: A translation matrix simply moves an object along with one or more of the three axes. A transformation matrix representing only translations has a simple form. If we have to translate a point P (x, y, z) by T_x on the X axis, T_y on the Y axis and T_z on the Z axis. We can define the translation matrix by:
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6. Transformation Matrix - Definition, Formula, Applications, Examples
Link: https://www.cuemath.com/algebra/transformation-matrix/
Description: The transformation matrix transforms a vector into another vector, which can be understood geometrically in a two-dimensional or a three-dimensional space. The frequently used transformations are stretching, squeezing, rotation, reflection, and orthogonal projection. Let us learn about some of these transformations in detail. Stretching.
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7. 2.6: The geometry of matrix transformations - Mathematics …
Link: https://math.libretexts.org/Bookshelves/Linear_Algebra/Understanding_Linear_Algebra_(Austin)/02%3A_Vectors_matrices_and_linear_combinations/2.06%3A_The_geometry_of_matrix_transformations
Description: Sep 17, 2022 · In this section, we will demonstrate how matrix transformations provide a convenient way to describe geometric operations, such as rotations, reflections, and scalings. We will then explore how matrix transformations are used in computer animation.
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8. Matrix transformations | Linear algebra | Math | Khan Academy
Link: https://www.khanacademy.org/math/linear-algebra/matrix-transformations
Description: Matrices can be used to perform a wide variety of transformations on data, which makes them powerful tools in many real-world applications. For example, matrices are often used in computer graphics to rotate, scale, and translate images and vectors.
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9. Transformation of Graphs Using Matrices - Translation - Varsity …
Link: https://www.varsitytutors.com/hotmath/hotmath_help/topics/transformation-of-graphs-using-matrices-translation
Description: Practice translating a graph using matrices. 1. If we have a ∆ XYZ where the coordinates are X(-4, 5) , Y(-4, 1) , and Z(-1, 1) , use matrices to shift the graph three units right and four units down. We'll first express the coordinates in the form of a matrix.
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10. Visual representation of transformation from matrix
Link: https://www.khanacademy.org/math/algebra-home/alg-matrices/alg-matrices-as-transformations/v/matrix-transformation-quadrilateral
Description: 10 years ago. So, if I try to generalize the properties we observe here, can we say the following ? - the upper left entree of the transformation matrix corresponds to a scaling on the x-axis. - the upper right entree of the transformation matrix corresponds to a translation on the x-axis.